# More Insight into Microscopic Properties of RN-AdS Black Hole Surrounded by Quintessence via an Alternative Extended Phase Space

## TL;DR

This paper investigates the phase transitions and microscopic properties of RN-AdS black holes surrounded by quintessence using an alternative extended phase space defined by charge squared and its conjugate, revealing critical behavior and thermodynamic singularities.

## Contribution

It introduces a novel extended phase space approach using charge squared and explores the microscopic structure via Ruppeiner geometry, providing new insights into black hole thermodynamics.

## Key findings

- Identifies critical points in the phase space of RN-AdS black holes with quintessence.
- Links Ruppeiner curvature singularities to phase transitions.
- Analyzes the thermodynamic behavior under the alternative phase space framework.

## Abstract

In this work we study the phase transition of the charged-AdS black hole surrounded by quintessence via an alternative extended phase space defined by the charge square $Q^2$ and her conjugate $\Psi$, a quantity proportional to the inverse of horizon radius, while the cosmological constant is kept fixed. The equation of state is derived under the form $Q^2=Q^2(T,\Psi)$ and the critical behavior of such black hole analyzed. In addition, we explore the connection between the microscopic structure and Ruppeiner geothermodynamics. We also find that, at certain points of the phase space, the Ruppeiner curvature is characterized by the presence of singularities that are interpreted as phase transitions.